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Monte Carlo

What fraction of the area of a square is closer to the center of the square than to any edge of the square? This one is harder than it looks! I am looking for an exact answer, but you can get a rough numerical estimate by a Monte Carlo method , and this might help you check your answer.

I have no idea where to begin this problem, and I need to provide clear explanation of why I choose to attempt the problem this way.

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UPDATE FROM OTA:
It seems like the question does'nt demand for Monte Carlo method and this method is ...

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